Finite Group DatabasebetaFinite Group Databasebeta| order | 8640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×AGL(2,𝔽3) |
| Fitting, socle | C32×C5 ⋊ C4×GL(2,𝔽3) |
| derived | C5×PSU(3,𝔽2)⋊C3 ⋊ C2×C4 |
| Sylow | C5 ⋊ C4×AGL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C5×PSU(3,𝔽2)⋊C3 | C2×C4 |
| Fitting, socle | C32×C5 | C4×GL(2,𝔽3) |
| prime radical | D5×AGL(2,𝔽3) | C2 |
| cosocle | D5×PSU(3,𝔽2)⋊C3 | C22 |
| LCS | G ▷ C5×PSU(3,𝔽2)⋊C3 | |
| UCS | C1 | |
492 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
55 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.